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Overlay networks achieve new functionality and enhance network performance by allowing routing to be controlled at the application layer. However, these approaches result in degradations of underlying networks due to the selfish behavior of overlay networks. In this paper, we investigate the stability of virtual network topology (VNT) control under the overlay networks that perform dynamic routing updates. We reveal that the dynamics of routing on overlay networks causes a high fluctuation in the traffic demand matrix, which leads to significant instability of VNT control. To overcome the instability induced by the overlay routing, we introduce hysteresis to the VNT control. Simulation results indicate that the hysteresis mechanism improves the network stability, but cannot always improve the network performance. We therefore extend the hysteresis mechanism and show that the proposed method improves both the network stability and the performance when the amount of traffic for overlay network is not large.